![Test scenario In order to comprehensively evaluate the performance of the proposed Cooperative Lane Change (CLC) controller, a sensitivity evaluation is designed based on the Level of Service (LOS) concept [37], as shown in TABLE I. LOS categorizes the quality of traffic flow and service provided to vehicles on a scale from A to F, with A representing the best performance and F representing the worst. The sensitivity evaluation assesses how the CLC controller performs across different levels of service. Each level of service corresponds to specific traffic conditions, such as traffic density, speed, and lane change difficulty. By evaluating the controller's performance under various LOS scenarios, a comprehensive understanding of its capabilities and limitations can be obtained.](https://www.researchgate.net/profile/Haoran-Wang-47/publication/374833061/figure/fig3/AS:11431281202052419@1698675684886/Test-scenario-In-order-to-comprehensively-evaluate-the-performance-of-the-proposed_Q320.jpg)
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Abstract— Lane-Change (LC) maneuvers are deemed to
jeopardize traffic safety, mobility, and sustainability. Cooperative
Lane-Change (CLC) solves this problem by accelerating the LC
process. This research proposes an optimal control based CLC
controller. It bears the following features: i) with the faster
completion of a CLC maneuver by making space and changing lane
at the same time; ii) with less speed oscillation perturbations on
traffic. To make space and change lane at the same time, a
formulation method in the relative spatial domain is proposed. In this
method, the conventional longitudinal and lateral coupled nonlinear
avoidance constraints are linearized into a relative longitudinal
distance fixed lateral-only avoidance constraint. Evaluations indicate
that the proposed method enhances the completion efficiency of
CLC by 15.67%, reduce traffic emission by 0.24%, reduce fuel
consumption by 0.36%, and improve traffic stability by 47.9%.
Index Terms— Cooperative lane-change, motion planning,
relative spatial domain, model predictive control.
I. INTRODUCTION
Lane-Change (LC) maneuvers are deemed to jeopardize
traffic safety, mobility, and sustainability [1, 2]. Past studies
have shown that LCs contribute to 60% of collisions on
highways, 20% more traffic speed oscillations, and more fuel
consumption [3]. These adverse effects are mainly due to the
44% more braking in LC maneuvers [4]. The rationale of the
braking in LC is that intent conflicts always exist among multi-
vehicles. The subject vehicle has to brake for searching a
yielding rival. The emerging cooperative automation
technology provides a potential solution to these problems.
Cooperative automation enables cooperation among
Connected and Automated Vehicles (CAVs) [5, 6]. It has
already shown its merits in enhancing traffic safety, mobility,
and sustainability [7]. By adopting this technology, the
Cooperative Lane-Change (CLC) scheme is proposed to
accelerate the LC process. An implementation scenario of
CLC is illustrated in Figure 1. The Subject Vehicle (SV) aims
at cutting into a gap between the Leading Vehicle (LV) and the
Rear Vehicle (RV). A CLC controller would regulate the speed
of the LV and the RV to make spaces for the SV to cut into the
target lane. This CLC process has been proven with potential
*Resrach supported by National Key R&D Program of China (No.
2022YFF0604905), Shanghai Automotive Industry Science and Technology
Development Foundation (No. 2213), Tongji Zhongte Chair Professor
Foundation (No. 000000375-2018082), Shanghai Sailing Program (No.
23YF1449600), Shanghai Post-doctoral Excellence Program (No.2022571),
and China Postdoctoral Science Foundation (No.2022M722405).
(Corresponding author: Jia Hu)
Haoran Wang and Jia Hu are with Key Laboratory of Road and Traffic
Engineering of the Ministry of Education, Tongji University, Shanghai
201804, China (e-mail: wang_haoran@tongji.edu.cn; hujia@tongji.edu.cn).
in enhancing LC completion efficiency and reducing
perturbations of LC on the traffic stream.
However, conventional CLC controllers cannot
accomplish a CLC maneuver efficiently. As illustrated in
Figure 1, conventional CLC controllers mostly conduct a CLC
maneuver through two steps: Space-Making (SM) and Lane-
Change (LC) [8-10]. In the SM step, an LC gap is produced by
the LV and RV. After a great enough gap has been made, the
SV would change into the gap. This two-step CLC tactic is
with low completion efficiency, since spatial and temporal
resources are wasted during the SV’s waiting for an LC gap.
The inefficient CLC maneuver may lead to greater
perturbations on traffic. Hence, a faster CLC tactic shall be
developed.
Figure 1. Conventional two-step CLC process
To make faster CLC maneuver, the one-step CLC tactic is
proposed. The intrinsic feature of this strategy is to make space
and change lane at the same time. Following this one-step CLC
tactic, past studies have proposed several CLC controllers [11-
13]. They are based on a shooting heuristic method. CLC
trajectories are planned by searching and connecting various
types of curves, including sine functions [11] and high-order
polynomial functions [12, 13]. However, these controllers can
only plan CLC trajectories with the same length, since the
planning horizon has to be fixed. Hence, these CLC controllers
lack adaptability in the real ever-changing environment.
Moreover, these shooting heuristic based methods cannot
consider the dynamics of vehicle. Hence, the generated
trajectory may not be fulfilled by local control. It may reduce
the execution accuracy and even lead to safety risks.
The research landscape in CLC has been significantly
influenced by learning-based methods, a popular topic among
recent studies [14-17]. These approaches leverage
reinforcement learning to determine multi-vehicle actions,
Wei Hao is with the School of Traffic and Transportation Engineering,
Changsha University of Science and Technology, Changsha 410114, China
(e-mail: haowei@csust.edu.cn).
Jaehyun So is with the Department of Transportation System Engineering,
Ajou University, Suwon-si, Gyeonggi-do, 16499, Republic of Korea (e-mail:
jso@ajou.ac.kr).
Zhijun Chen is with the Intelligent Transportation Systems Research
Center, Wuhan University of Technology, Wuhan 430063, China (e-mail:
chenzj556@whut.edu.cn).
A Faster Cooperative Lane Change Controller Enabled by
Formulating in Spatial Domain*
Haoran Wang, Wei Hao, Jaehyun So, Zhijun Chen, and Jia Hu, Member, IEEE
showing adaptability to diverse scenarios [14-16]. Nonetheless,
learning-based methods are restricted to planning behavioral
decisions, lacking the ability to generate CLC trajectories with
specific vehicle control commands. Addressing this limitation,
Zhang et al. introduced a hybrid model predictive control
method that formulates and tackles the CLC planning problem
using machine learning techniques [17]. This highlights the
potential superiority of optimal control-based methods for
CLC planning.
The optimal control-based approach offers the capability
to plan trajectories for multiple vehicles while taking into
account their execution capabilities [18-23]. Traditional
optimal control-based CLC controllers have been constrained
by vehicle dynamics or kinematics constraints [9, 10],
ensuring precise execution. However, these controllers rely on
a two-step CLC tactic, as depicted in Figure 1. Consequently,
there is a need to develop an optimal control-based one-step
CLC controller to enable quicker CLC maneuvers.
Towards the optimal control based one-step CLC
controller, the key challenge is high computation complexity
due to integers mixed collision avoidance constraints of the
longitudinal and lateral coupled planning [24, 25].
Conventionally, longitudinal and lateral distance constraints
are used by assuming that vehicles are rectangles. Hence,
collisions could be avoided if any one of the longitudinal and
lateral constraints is satisfied. To be adaptive to general
scenarios, it needs at least three binary variables (0 or 1) at
each control step to make an optimal choice between the
longitudinal and lateral constraints. Too many binary variables
reduce computation efficiency and impede the real-time
implementation.
In this research, an optimal control based CLC controller
is proposed to make a faster CLC maneuver. The proposed
method bears following features:
With the faster completion of a CLC maneuver by
making space and changing lane at the same time;
With less speed oscillation perturbations on traffic;
This paper is organized as follows. Section II provides the
research scope. Section III formulates the proposed CLC
controller in the relative spatial domain. Section IV presents
solution algorithms. Section V makes an evaluation for the
proposed method. Section VI concludes the research and
provides future directions.
II. HIGHLIGHTS
The objective of the proposed CLC controller is to make a
faster completion of the CLC maneuver. The highlights lie in
its control logic and problem formulations:
Making space and changing lane at the same time:
The proposed method adopts the one-step CLC tactic. It
enables to make space and change lane at the same time.
Hence, a faster completion of a CLC maneuver is received. It
may reduce the influence of LC maneuvers on traffic.
Reducing computation complexity by formulating in
the relative spatial domain: To simultaneously create space
and change lanes, it is essential to employ longitudinal and
lateral coupled planning. It leads to nonlinear collision
avoidance constraints in the temporal domain, since a choice
shall be made between the longitudinal collision avoidance
and lateral collision avoidance. This increases the
computation complexity. To linearize collision avoidance
constraints, a problem formulation method in the relative
spatial domain is proposed in this research. It transforms the
conventional temporal domain based trajectory planning into
the relative spatial domain based trajectory planning. At a
fixed relative distance, only lateral collision avoidance
constraint is needed. The linearization greatly enhances
computation efficiency.
Applying a time-varying desired state to accelerate
the completion: During the formulation of the optimal
control problem, a dynamically changing desired state is
designed. This allows for efficiently guiding the SV to swiftly
navigate into the gap while simultaneously creating space.
This design would speed up the CLC process and enhance
CLC completion efficiency.
Balancing objectives between CLC completion
efficiency and traffic stability: The cost function involves
target error cost and speed oscillation cost. The target error
cost is minimized to enhance CLC completion efficiency. The
speed oscillation cost is minimized to ensure traffic stability.
The balance between CLC completion efficiency and traffic
stability could be achieved in real implementations, by
customizing weighting factor settings.
III. PROBLEM FORMULATION
The primary objective of the proposed controller is to
execute a quicker CLC maneuver by simultaneously making
space and changing lanes. Figure 2 illustrates a typical
application scenario where the SV needs to change lanes and
exit from an off-ramp, but encounters insufficient gap
availability in the target lane. In such situations, the proposed
CLC controller can be activated to facilitate the maneuver. It
effectively coordinates the LV and RV to generate space for
lane change while also guiding the SV through the lane-change
process.
Figure 2. A typical CLC scenario
A. Definition and Rational of Relative Spatial Domain
To realize the objective of making space and changing lane
at the same time, a formulation method in the relative spatial
domain is proposed in this research. The rational of the relative
spatial domain is presented in this section.
Conventionally, vehicle control problem is formulated in
the temporal domain [26-28]. However, these formulation
methods face challenges on computation complexity in CLC
scenarios, since nonlinearity exist. In the CLC problem,
longitudinal and lateral collision avoidance constraints are
needed in the planning of multi-vehicles (LV, RV, and SV).
Two choices are needed, including longitudinal or lateral
collision avoiding, and in front or back of the target vehicle.
Hence, at least two binary variables (0 or 1) are needed in each
control step to optimally make choices. The integers mixing
leads to low computation efficiency.
However, in the relative spatial domain, much fewer
binary variables are needed. Instead of using time as the
independent variable, the relative longitudinal position
between vehicles is employed in the formulation. At a relative
longitudinal position, whether longitudinal collisions exist or
not is decided. Only lateral collision avoidance constraint is
needed when the relative longitudinal position is unsafe.
Hence, there are no more binary variables in the collision
avoidance constraint.
The relative reference frame is defined in Figure 3. The
definition of reference frame considers two types of scenarios:
(a) the SV starts CLC from the rear of the gap; (b) the SV starts
CLC from the front of the gap. In the relative reference frame,
the right road boundary is set as the origin of the Y-axis. In the
scenario (a), the longitudinal position of the RV is used as the
origin of the X-axis. In the scenario (b), the longitudinal
position of the LV is used as the origin of the X-axis.
In the two scenarios, problem formulations are nearly the
same. In the implementation, the reference frame could be
selected according to the real-time status when the CLC
system is activated. Hence, this paper takes the scenario (a) as
an example and presents the formulation in the following
manuscript. In the scenario (a), position states of vehicles are
expressed as follows. is the longitudinal distance between
the SV and RV. is the longitudinal distance between the LV
and RV. represents the lateral distance between the SV and
the right road boundary. denotes the lateral distance
between the LV and the right road boundary. is lateral
distance between the RV and the right road boundary.
Figure 3. The relative reference frame
B. State Definition in Relative Spatial Domain
Within the context of the relative spatial domain, the CLC
system state vector and control vector are defined in the
following manner.
[,
,
,
,
,
,
,
]
(1)
[,,,]
(2)
where is the acceleration; represents the heading angle in
the Frenet coordinate system; denotes the front steering
angle, as illustrated in Figure 4. is the relative speed. They
are defined in the following manner.
(3)
(4)
(5)
(6)
(7)
(8)
where in the Frenet coordinate system, refers to the
longitudinal position of the LV; represents the longitudinal
position of the SV; denotes the longitudinal position of the
RV; signifies the speed of the LV; denotes the speed of
the SV; represents the speed of the RV.
Figure 4. Vehicle dynamics notation in the frenet coordinate
C. System Dynamics Modeling in Relative Spatial Domain
System dynamics are modeled in the relative spatial
domain. The formulation derives from the modeling in the
conventional temporal domain. It is then discretized and
transformed into the spatial domain in the relative reference
frame.
1) System dynamics in temporal domain
In the conventional temporal domain, a vehicle kinematics
model is generally formulated in the frenet coordinate as
follows [26].
= (9)
= (10)
= (11)
=
(12)
where denotes the distance between the front axle and the
rear axle, as illustrated in Figure 4; is the road curvature.
In a CLC maneuver, the LV and RV are longitudinally
moving along lane centerline. The SV moves laterally to
change lane. Therefore, based on the vehicle kinematics model
in equations (9)-(12), the system dynamics of LV, SV, and RV
are modeled into equations (13)-(20).
= (13)
= (14)
= (15)
= (16)
= (17)
= (18)
=
(19)
= (20)
2) System dynamics in the relative spatial domain
In the relative reference frame as defined in Figure 3, the
longitudinal maneuver of the SV and LV is the relative motion
against the RV. Therefore, system dynamics in the relative
reference are derived based on equations (13)-(20) as follows.
=
(21)
= (22)
= (23)
= (24)
=
(25)
= (26)
= (27)
Since the vehicle control problem is generally
implemented by executing stepwise commands, the system
dynamics shall be discretized. By applying the forward Euler
method [29], the system dynamics in equations (21)-(27) could
be discretized as follows.
=
+
(28)
=
+
(29)
=
+
(30)
=
+
(31)
=
+
(32)
=+
(33)
=
+
(34)
where is the length of time-step; is the index of control
step.
Equation (31) gives that =
. We define a
relative space step as =
=
. Therefore,
=
> 0
< 0. It is discontinuous since
0.
To prevent this discontinuity, a small enough constant is
introduced as
[27]. Hence,
=()=
=
1
+,
0
=1
,
< 0
(35)
where is the relative slowness of vehicle which derived
from the definition of slowness in the authors’ previous studies
[30, 31]. Since is a small enough constant, it will not affect
the computation of
. Therefore, =
is adopted in the
following formulations for more concise expression. Equation
(35) provides the rule of transforming system dynamics from
the conventional temporal domain to the proposed relative
spatial domain.
In the relative spatial domain, the global time is set as a
new state variable. It follows a propagation rule as follows.
=+=
+
0
< 0
(36)
The difference between
0 and
< 0 makes the
system dynamics as a hybrid model [32]. A hybrid Model
Predictive Control (MPC) problem is generally solved by
using a binary selection variable [33]. By defining as
1
0
0
< 0 and substituting the equation (35) into the
equations (28)-(34) and (36), the system dynamics are
modeled into the relative spatial domain as follows.
=
+
+
= 1
+
+
= 0
(37)
where
=+
,
=
(38)
=
,
=
(39)
=,
=
(40)
=
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
00 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0
0 0
0 0 0 0 0 0 0 0
(41)
=
0 0 0 0
0 0 0
00 0
0 0 0 0
0 0 0 0
0 0 0
0 0 0 0
0 0
0
(42)
=
[
, 0,0,0,0,
, 0,0
]
(43)
It should be noticed that the substitution of equation (35)
into the equations (28)-(34) and (36) does not influence the
system’s operational domain. Moreover, coefficient matrices
in equation (37) are time-varying. It leads to a time-varying
hybrid MPC problem. The solving method is discussed
detailly in the section IV.
D. Desired State Design for Accelerating CLC Process
The control objective of the proposed controller is to
expedite the system's approach towards the desired state as
rapidly as possible. The desired state is defined as follows.
[
,
,
,
,
,
,
]
(44)
The design of variables in equation (44) is based on two
considerations, CLC maneuver target and CLC process
accelerating.
In the target status, the LV, SV, and RV are stably cruising
on the designated lane. Hence, the following desired variables
are set.
0
(45)
0
(46)
0
(47)
(48)
where
represents the desired relative speed of the LV;
denotes the desired relative speed of the SV; is the
desired following headway distance;
is the desired
heading in the frenet coordinate;
is the desired cruising
speed.
The desired relative distance
between the LV and RV
is set as a space that enables stable cruising with the SV cut-in.
2
(49)
To accelerate the CLC process and reach a one-step CLC
tactic, the desired lateral position of SV is particularly
designed. In the one-step CLC tactic, space-making and lane-
changing are conducted at the same time. The ideal process is
that the SV cuts into the gap at the time when the space has
just been produced.
Figure 5. Time-varying desired state function
This CLC process accelerating method is achieved by a
time-varying desired lateral position of SV, illustrated in
Figure 5. The formulation is as follows.
If min
,
< 1 (the red line in Figure 5)
()
=+ min
,+
+,
(50)
,
=min
(
,
)
= 1
max(
,
)+
=1
(51)
else (the blue line in Figure 5)
= (52)
where is the initial lateral position of SV; ,
() is
the lateral position that ensures the safe lateral distance against
LV and RV; is the lateral position of the target lane
centerline; is the lateral position of LV. is the lateral
position of RV; is a lane-change command at the higher
layer. equals 1 for a left lane-change and -1 for a right lane-
change; is the lateral position of the target lane’s
centerline.
is the safe lane-change gap in front of the
SV;
is the safe lane-change gap at the rear of the SV.
They are computed as follows [26, 27].
+
×
2
+
2
+ (53)
+
×
2
+
2
+ (54)
where
is the reaction time of CAV;
is the braking
control delay; is the minimum acceleration; is the
length of a vehicle.
E. Constraints and Their Linearization
1) Collision avoidance constraints
Collision avoidance constraints are established by
controlling and maintaining appropriate longitudinal and
lateral distances between vehicles. Collisions between the LV,
SV, and RV are avoided by the inner collision avoidance
constraints. Collisions between LV/SV/RV and the
surrounding vehicles are avoided by the outer collision
avoidance constraints.
(1) Inner collision avoidance constraints: In order to avoid
collision between the LV, SV, and RV, an inner collision
avoidance constraint shall be formulated.
Previous studies mostly regard vehicles as rectangles.
Collision avoidance is achieved if one of the following
conditions is satisfied: i) The longitudinal distance between
two vehicles is required to be greater than the safe distance. ii)
The lateral distance between two vehicles is required to be
greater than the safe distance. The mathematical formulation
is as follows.
()
()
or ()()
(55)
Equation (55) is nonlinear, since choices have to be made
between different constraints. The proposed formulation
method in the relative spatial domain leads to a linear collision
constraint. In the relative spatial domain, the relative
longitudinal space is set as the independent variable. The
collision avoidance constraint is as follows.
, where
<
<
(56)
It means that equation (56) is activated only when
<<
that is in accordance to the control index
in the relative spatial domain. Hence, the constraint in equation
(56) is linear. It reduces computation complexity compared to
the conventional formulation method in equation (55), where
at least two binary variables are needed to make choices [27].
Although there is still one binary variable in the selection of
hybrid system dynamics model in equation (37), the proposed
method removes half binary variables in the whole planning
horizon. It would greatly enhance computation efficiency,
since the increase in the number of binary variables
exponentially enhances computation complexity [34].
Moreover, between the LV and SV, longitudinal gap shall
be regulated as follows.
+
(57)
where
and could be easily computed via the
accumulation of speed , , and in the state vector.
In the scenario illustrated by Figure 3 (b), states of RV
would be introduced into the state vector when LV is set as the
reference object. Therefore, the longitudinal gap between the
SV and RV shall be regulated as follows.
+
(58)
(2) Outer collision avoidance constraints: In the traffic
context, the longitudinal movements of the LV and SV are
constrained to prevent collisions with nearby vehicles, such as
the Preceding Vehicle on the Original Lane (PV-I) and the
Preceding Vehicle on the Target Lane (PV-T), as shown in
Figure 2. The longitudinal distances between PV-I, SV, LV,
and PV-T are constrained as follows.
(59)
(60)
where
is the relative longitudinal position of PV-I;
is the relative longitudinal position of PV-T. The future
positions of PV-I and PV-T are inputted based on the
assumption that speeds of the PV-I and PV-T are unchanged.
It is reasonable since the speeds of surrounding vehicles
remain relatively stable over a short period.
2) System Limit Constraints
Vehicles are required to remain within the boundaries of
the road geometry while traveling.
(61)
The acceleration of the vehicle should be limited within the
bounds determined by the vehicle's capability and comfort
level.
{
,
,
}
(62)
The front-wheel angle of the vehicle should remain within
its steering range to ensure proper maneuverability.
(63)
F. Cost Function
The cost function is expressed in a quadratic form as
equation (64).
min
1
2
,,+
1
2
(64)
where and are diagonal matrices consisting of non-
negative weighting factors. They are defined as follows.
diag
,
,
,
,
,
,
(65)
diag
,
,
,
(66)
where represents the weighting factor for the speed error
cost of the LV; represents the weighting factor for the speed
error cost of the SV.
represents the weighting factor for the
position error cost of the SV.
represents the weighting
factor for the heading error cost of the SV.
represents the
weighting factor for the lateral position error cost of the SV.
represents the weighting factor for the speed oscillation
cost of the RV.
represents the weighting factor for the
acceleration effort cost of the LV. represents the weighting
factor for the acceleration effort cost of the RV. represents
the weighting factor for the acceleration effort cost of the SV.
represents the weighting factor for the steering effort cost
of the SV.
The objective function (64) is a balance between multi-
objectives, including CLC completion efficiency, speed
stability, and trajectory smoothness. CLC completion
efficiency is considered by
,
. Speed stability
is considered by
,
,
,
,
,
. Trajectory smoothness is considered by
. Users could customize the weighting factors in
equation (64) to meet their preferences.
IV. PROBLEM SOLVING
A. Full Problem Summary
The full problem is summarized as follows. It is a time-
varying hybrid MPC problem.
min
1
2,,+
1
2
s.t. =
+
+
= 1
+
+
= 0
, where
<<
+
{
,
,
}
(67)
B. Solving Algorithm
The time-varying hybrid MPC problem is solved by a
solving mechanism as illustrated in Figure 6. It consists of
three modules. The outer scheme is the Branch and Bound
(B&B) method [35]. It is a typical solving method for hybrid
MPC problems [33]. The upper-layer is an iteration algorithm
[31, 36]. By using the optimized state from the last iteration as
the input, the iteration algorithm is capable of handling the
time-varying coefficients in equation (37).
Figure 6. Solving mechanism
The lower layer in Figure 6 is a Dynamic Programming
(DP) based solver. It is developed specifically for the quadratic
MPC problem by the authors in previous studies [26-28]. It
computes the optimal solution by backward calculating
concomitant matrices and forward calculating control vector
and state vector. The DP solver is presented in Algorithm 1.
Algorithm 1 Dynamic Programming based solver
Input: initial state
,
, ,
Output: optimal control and state for each step
1. Initialize: , , and
2. For terminal step =:
(68)
(69)
3. Backward calculating concomitant matrices
For {1, ,1}:
=,
(70)
=
+
+
(71)
=
+
+
+
(72)
with
= (+
)
(73)
=
(74)
=
+
(75)
=+
(76)
=+
(77)
4. Forward calculating control vector and state vector
For {0,1, ,1}:
=+
(78)
=+
(79)
V. EVALUATION
The proposed CLC controller is assessed and evaluated
based on the following aspects: i) function validation; ii)
completion efficiency evaluation; iii) quantification of
influences on traffic.
A. Experiment Design
The test scenario depicted in Figure 7 involves a Connected
and Automated Vehicle (CAV), referred to as SV, traveling
on the left lane within a traffic environment. The SV needs to
exit from an off-ramp, necessitating a mandatory lane change.
The successful execution of the lane change maneuver
requires coordination between the SV and two other CAVs,
known as LV and RV, present on the right lane.
This scenario serves as a practical testbed to assess the
performance and effectiveness of the proposed CLC
controller in a real-world traffic situation. In this scenario, the
proposed CLC controller is evaluated by controlling the three
CAVs (SV, LV, and RV) to perform the necessary lane
change maneuver. The controller aims to ensure smooth and
safe coordination among the vehicles during the lane change
process, enabling the SV to successfully transition to the
desired off-ramp exit.
Figure 7. Test scenario
In order to comprehensively evaluate the performance of
the proposed Cooperative Lane Change (CLC) controller, a
sensitivity evaluation is designed based on the Level of
Service (LOS) concept [37], as shown in TABLE I. LOS
categorizes the quality of traffic flow and service provided to
vehicles on a scale from A to F, with A representing the best
performance and F representing the worst.
The sensitivity evaluation assesses how the CLC controller
performs across different levels of service. Each level of
service corresponds to specific traffic conditions, such as
traffic density, speed, and lane change difficulty. By
evaluating the controller's performance under various LOS
scenarios, a comprehensive understanding of its capabilities
and limitations can be obtained.
TABLE I SENSITIVIT Y DEFINITION
case 1
case 2
case 3
case 4
case 5
case 6
LOS
A
B
C
D
E
F
(/)
12
16
25
36
55
67
()
134
101
64
45
29
24
(/)
30
27
25
23
17
13
()
4.5
3.7
2.6
2
1.7
1.8
where is the traffic density; is the average following
gap; is the traffic speed; is the average traffic
headway.
In order to test the traffic stabilizing function of the
proposed CLC controller. A speed perturbation case is
designed in Figure 8. In this case, the PV-I and PV-T are with
a speed perturbation in the CLC process. LOS is set to F.
Figure 8. Speed perturbation on the PV-T and PV-I
B. Controller Types
In this experiment, the performance and effectiveness of
the proposed Cooperative Lane Change (CLC) system are
0 10 20 30 40
Time (s)
0
5
10
15
Speed (m/s)
evaluated using three different controllers. These controllers
are as follows:
Proposed CLC controller (CLC-1): The proposed CLC
controller conducts the space-making and lane-change
maneuver at the same time. It is an optimal control based
controller.
Baseline CLC controller (CLC-2): It is the conventional
optimal control based CLC controller. It has to conduct a lane-
change after a great-enough gap has been made.
Baseline human driver (IDM): The Intelligent Driver
Model (IDM) [38] is adopted as a baseline to simulate human
driving behaviors in cut-in maneuvers. The IDM is a well-
known and widely used model in the field of traffic simulation
and cooperative driving research. The vehicle has to squeeze
into the target lane to make a lane-change.
C. Parameter Setting
The following settings are adopted.
Lane width: 3 m;
Desired speed: 20 m/s;
Vehicle length : 5 m;
Time step : 0.02 s;
Desired car following headway: 1.1 s.
Acceleration range: [5,3] m/s;
Steering angle range: [450°,450°];
CAV reaction time
: 0.5 s;
Braking control delay
: 0.35 s;
Minimum following headway between the LV and the
PV-T: 0.5 s;
HV reaction time
: 1.5 s;
IDM controller is set according to [39].
D. Measure of Effectiveness
Measures of Effectiveness (MOEs) are as follows.
Function validation: To verify the function of the
proposed Cooperative Lane Change (CLC) controller, the
vehicle trajectories are analyzed and compared. The one-step
CLC tactic, which involves making space and changing lanes
simultaneously, is the key aspect of the proposed controller's
function.
CLC completion efficiency: This MOE is quantified by
the completion time of a CLC process.
Influences on traffic: This MOE is quantified from
three aspects:
1) Emissions: CO2 emission, CO emission, HC
emission, and NOx emission per meter;
2) Fuel consumption per meter;
3) Speed stability: This MOE is quantified by the
speed oscillation rate :
max(
,
)
(80)
E. Experiment Results
Results demonstrate that compared to the conventional
CLC controller, the proposed CLC controller: i) is capable of
making space and change lane at the same time; ii) enhances
CLC completion efficiency by 15.67%; iii) reduces traffic
emissions by 0.24% and fuel consumption by 0.36%; iv)
reduces traffic oscillation by 47.9%; v) has an average
computation time of 1.30 milliseconds.
1) Function validation
The CLC function is validated by vehicles’ sample
trajectories, as illustrated in Figure 9. It shows that the
proposed controller is capable of conducting a CLC maneuver
in all LOS levels, as shown in the first column of Figure 9.
Moreover, all CLC maneuvers are verified without collisions,
as illustrated in Figure 10. It demonstrates the function of CLC
for the proposed controller.
Figure 9. Sample trajectories in all LOS levels
Figure 10. Following headway trajectories
Figure 11. The function validation
The function of making space and changing lane at the
same time is verified in Figure 11. As shown in Figure 11 (I)(b),
the proposed controller starts to make space and change lane
at the same time at the time when the CLC system is activated.
Nevertheless, the baseline CLC-2 controller has to wait for a
great-enough lane-change gap, as shown in Figure 11 (II)(b).
A human driver has to wait for the give-in of the rear vehicle,
as shown in Figure 11 (III)(b).
2) CLC completion efficiency
The CLC completion efficiency is quantified by the CLC
completion time in Figure 12. Results show that the proposed
controller (CLC-1) enhances CLC completion efficiency by
15.67% compared to the baseline CLC controller (CLC-2),
and 206.92% compared to a human driver.
A sensitivity analysis is conducted for CLC completion
efficiency in terms of LOS levels, as illustrated in Figure 12.
It demonstrates that the proposed method shows superiority in
lower LOS-level situations. When the LOS level is A, all three
controllers have a similar CLC completion efficiency. When
the LOS level is greater than B, human drivers’ lane-change
efficiency greatly deteriorates, since it wastes more time in
waiting for the give-in of the rear vehicle in dense traffic.
When the LOS level is greater than D, the superiority of the
proposed controller is prominent against the baseline CLC
controller (CLC-2). The rationale for the superiority in lower
LOS-level traffic for the proposed controller lies in two aspects.
First, the proposed method is enabled to make space and
change lane at the same time, as aforementioned by the
trajectories in Figure 11. Second, the proposed method is more
effective in the process of space-making. As illustrated in
Figure 11 (I)(d), the proposed controller is enabled to make
space by both maneuvering the LV to accelerate and the RV to
decelerate. This leads to faster completion of space-making.
However, the baseline controller and human driver can only
rely on the give-in of the RV, as illustrated in Figure 11 (II)(d)
and (III)(d).
Figure 12. CLC completion efficiency
3) Influences on traffic
The proposed CLC controller is proven to enhance traffic
sustainability, as illustrated in Figure 13. Compared to human
drivers, the proposed method reduces traffic emission by 1.42%
and fuel consumption by 3.08%. Compared to the
conventional CLC-2 controller, the proposed controller
reduces traffic emission by 0.24% and fuel consumption by
0.36%. The rationale of the sustainability enhancement lies in
the highlight of the proposed controller: with less speed
oscillation perturbations on traffic. This has been confirmed in
our evaluation. As shown in the Figure 11 (d), the proposed
controller has significantly less speed oscillations of the RV. It
indicates that the CLC maneuver casts less perturbations on
upstream traffic.
A sensitivity analysis is conducted for the sustainability
enhancement in regard to LOS levels, as illustrated in Figure
13. Results indicate that the sustainability enhancement of the
proposed controller is particularly significant in lower LOS-
level traffic. This finding is in line with the results of
sensitivity analysis on completion efficiency.
Figure 13. Traffic emission and consumption benefits (CLC-1 vs CLC-2)
The proposed controller is proven with the capability of
enhancing traffic stability, as demonstrated by Figure 14.
Results show that the proposed controller reduces traffic speed
oscillations by 47.9% compared to the conventional CLC
controller and 90.5% compared to the human driver. As
illustrated in Figure 14 (I) and (IV), under the control of the
proposed controller, traffic speed oscillations are eliminated at
the seventh upstream vehicle. However, when a human makes
a cut-in maneuver, traffic waves propagate for 50 seconds and
finally stop at the twenty-fifth vehicle, as shown in Figure 14
(III) and (IV). It reveals the rationale of how CLC tactics
would avoid negative effects of cut-in maneuvers on traffic.
Figure 14. Vehicle trajectories and oscillation propagation
VI. CONCLUSION AND FUTURE RESEARCH
This research proposes an optimal control based CLC
controller. It bears the following features: i) with the faster
completion of a CLC maneuver by making space and changing
lane at the same time; ii) with less speed oscillation
perturbations on traffic. To make space and change lane at the
same time, a formulation method in the relative spatial domain
is proposed. In this method, the conventional longitudinal and
lateral coupled nonlinear avoidance constraints are linearized
into a relative longitudinal distance fixed lateral-only
avoidance constraint. Evaluations show that:
The proposed controller enhances CLC completion
efficiency by 15.67% compared to a baseline CLC controller.
This improvement indicates that the proposed controller can
facilitate faster and more efficient lane-change maneuvers,
reducing the time required to complete the maneuver.
The proposed CLC controller is confirmed to reduce
traffic emissions by 0.24% and fuel consumption by 0.36%.
This reduction in emissions and fuel consumption suggests
that the controller's optimized control strategy leads to more
eco-friendly driving behaviors, resulting in environmental
benefits.
The proposed CLC controller is demonstrated to reduce
traffic oscillations by 47.9%. This reduction in traffic
oscillations indicates that the controller can effectively
mitigate fluctuations in vehicle speeds and maintain smoother
traffic flow, contributing to improved overall traffic stability
and safety.
In the current research, the proposed controller assumes
states of background vehicles are not changed rapidly in a
short prediction. Future research efforts could focus on more
accurate methods for the prediction of background vehicles.
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